Simultaneous class discovery and classification of microarray data using spectral analysis

Maximum Likelihood Estimation of GEVD: Applications in Bioinformatics

We propose a method, maximum likelihood estimation of generalized eigenvalue decomposition (MLGEVD) that employs a well known technique relying on the generalization of singular value decomposition (SVD). The main aim of the work is to show the tight equivalence between MLGEVD and generalized ridge regression. This relationship reveals an important mathematical property of GEVD in which the second argument act as prior information in the model. Thus we show that MLGEVD allows the incorporation of external knowledge about the quantities of interest into the estimation problem. We illustrate the importance of prior knowledge in clinical decision making/identifying differentially expressed genes with case studies for which microarray data sets with corresponding clinical/literature information are available. On all of these three case studies, MLGEVD outperformed GEVD on prediction in terms of test area under the ROC curve (test AUC). MLGEVD results in significantly improved diagnosis, prognosis and prediction of therapy response.

New bandwidth selection criterion for Kernel PCA: approach to dimensionality reduction and classification problems

BACKGROUND

DNA microarrays are potentially powerful technology for improving diagnostic classification, treatment selection, and prognostic assessment. The use of this technology to predict cancer outcome has a history of almost a decade. Disease class predictors can be designed for known disease cases and provide diagnostic confirmation or clarify abnormal cases. The main input to this class predictors are high dimensional data with many variables and few observations. Dimensionality reduction of these features set significantly speeds up the prediction task. Feature selection and feature transformation methods are well known preprocessing steps in the field of bioinformatics. Several prediction tools are available based on these techniques.

RESULTS

Studies show that a well tuned Kernel PCA (KPCA) is an efficient preprocessing step for dimensionality reduction, but the available bandwidth selection method for KPCA was computationally expensive. In this paper, we propose a new data-driven bandwidth selection criterion for KPCA, which is related to least squares cross-validation for kernel density estimation. We propose a new prediction model with a well tuned KPCA and Least Squares Support Vector Machine (LS-SVM). We estimate the accuracy of the newly proposed model based on 9 case studies. Then, we compare its performances (in terms of test set Area Under the ROC Curve (AUC) and computational time) with other well known techniques such as whole data set + LS-SVM, PCA + LS-SVM, t-test + LS-SVM, Prediction Analysis of Microarrays (PAM) and Least Absolute Shrinkage and Selection Operator (Lasso). Finally, we assess the performance of the proposed strategy with an existing KPCA parameter tuning algorithm by means of two additional case studies.

CONCLUSION

We propose, evaluate, and compare several mathematical/statistical techniques, which apply feature transformation/selection for subsequent classification, and consider its application in medical diagnostics. Both feature selection and feature transformation perform well on classification tasks. Due to the dynamic selection property of feature selection, it is hard to define significant features for the classifier, which predicts classes of future samples. Moreover, the proposed strategy enjoys a distinctive advantage with its relatively lesser time complexity.

Systems analysis of high-throughput data

Modern high-throughput assays yield detailed characterizations of the genomic, transcriptomic, and proteomic states of biological samples, enabling us to probe the molecular mechanisms that regulate hematopoiesis or give rise to hematological disorders. At the same time, the high dimensionality of the data and the complex nature of biological interaction networks present significant analytical challenges in identifying causal variations and modeling the underlying systems biology. In addition to identifying significantly disregulated genes and proteins, integrative analysis approaches that allow the investigation of these single genes within a functional context are required. This chapter presents a survey of current computational approaches for the statistical analysis of high-dimensional data and the development of systems-level models of cellular signaling and regulation. Specifically, we focus on multi-gene analysis methods and the integration of expression data with domain knowledge (such as biological pathways) and other gene-wise information (e.g.,  sequence or methylation data) to identify novel functional modules in the complex cellular interaction network.

SC(3): Triple spectral clustering-based consensus clustering framework for class discovery from cancer gene expression profiles

In order to perform successful diagnosis and treatment of cancer, discovering, and classifying cancer types correctly is essential. One of the challenging properties of class discovery from cancer data sets is that cancer gene expression profiles not only include a large number of genes, but also contains a lot of noisy genes. In order to reduce the effect of noisy genes in cancer gene expression profiles, we propose two new consensus clustering frameworks, named as triple spectral clustering-based consensus clustering (SC3) and double spectral clustering-based consensus clustering (SC2Ncut) in this paper, for cancer discovery from gene expression profiles. SC3 integrates the spectral clustering (SC) algorithm multiple times into the ensemble framework to process gene expression profiles. Specifically, spectral clustering is applied to perform clustering on the gene dimension and the cancer sample dimension, and also used as the consensus function to partition the consensus matrix constructed from multiple clustering solutions.Compared with SC3, SC2Ncut adopts the normalized cut algorithm, instead of spectral clustering, as the consensus function.Experiments on both synthetic data sets and real cancer gene expression profiles illustrate that the proposed approaches not only achieve good performance on gene expression profiles, but also outperforms most of the existing approaches in the process of class discovery from these profiles.

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Multi-gene interactions likely play an important role in the development of complex phenotypes, and relationships between interacting genes pose a challenging statistical problem in microarray analysis, since the genes involved in these interactions may not exhibit marginal differential expression. As a result, it is necessary to develop tools that can identify sets of interacting genes that discriminate phenotypes without requiring that the classification boundary between phenotypes be convex.

Results

We describe an extension and application of a new unsupervised statistical learning technique, known as the Partition Decoupling Method (PDM), to gene expression microarray data. This method may be used to classify samples based on multi-gene expression patterns and to identify pathways associated with phenotype, without relying upon the differential expression of individual genes. The PDM uses iterated spectral clustering and scrubbing steps, revealing at each iteration progressively finer structure in the geometry of the data. Because spectral clustering has the ability to discern clusters that are not linearly separable, it is able to articulate relationships between samples that would be missed by distance- and tree-based classifiers. After projecting the data onto the cluster centroids and computing the residuals ("scrubbing"), one can repeat the spectral clustering, revealing clusters that were not discernible in the first layer. These iterations, each of which provide a partition of the data that is decoupled from the others, are carried forward until the structure in the residuals is indistinguishable from noise, preventing over-fitting. We describe the PDM in detail and apply it to three publicly available cancer gene expression data sets. By applying the PDM on a pathway-by-pathway basis and identifying those pathways that permit unsupervised clustering of samples that match known sample characteristics, we show how the PDM may be used to find sets of mechanistically-related genes that may play a role in disease. An R package to carry out the PDM is available for download.

Conclusions

We show that the PDM is a useful tool for the analysis of gene expression data from complex diseases, where phenotypes are not linearly separable and multi-gene effects are likely to play a role. Our results demonstrate that the PDM is able to distinguish cell types and treatments with higher accuracy than is obtained through other approaches, and that the Pathway-PDM application is a valuable technique for identifying disease-associated pathways.

Discovering biological progression underlying microarray samples

In biological systems that undergo processes such as differentiation, a clear concept of progression exists. We present a novel computational approach, called Sample Progression Discovery (SPD), to discover patterns of biological progression underlying microarray gene expression data. SPD assumes that individual samples of a microarray dataset are related by an unknown biological process (i.e., differentiation, development, cell cycle, disease progression), and that each sample represents one unknown point along the progression of that process. SPD aims to organize the samples in a manner that reveals the underlying progression and to simultaneously identify subsets of genes that are responsible for that progression. We demonstrate the performance of SPD on a variety of microarray datasets that were generated by sampling a biological process at different points along its progression, without providing SPD any information of the underlying process. When applied to a cell cycle time series microarray dataset, SPD was not provided any prior knowledge of samples' time order or of which genes are cell-cycle regulated, yet SPD recovered the correct time order and identified many genes that have been associated with the cell cycle. When applied to B-cell differentiation data, SPD recovered the correct order of stages of normal B-cell differentiation and the linkage between preB-ALL tumor cells with their cell origin preB. When applied to mouse embryonic stem cell differentiation data, SPD uncovered a landscape of ESC differentiation into various lineages and genes that represent both generic and lineage specific processes. When applied to a prostate cancer microarray dataset, SPD identified gene modules that reflect a progression consistent with disease stages. SPD may be best viewed as a novel tool for synthesizing biological hypotheses because it provides a likely biological progression underlying a microarray dataset and, perhaps more importantly, the candidate genes that regulate that progression.

We present a novel computational approach, Sample Progression Discovery (SPD), to discover biological progression underlying a microarray dataset. In contrast to the majority of microarray data analysis methods which identify differences between sample groups (normal vs. cancer, treated vs. control), SPD aims to identify an underlying progression among individual samples, both within and across sample groups. We validated SPD's ability to discover biological progression using datasets of cell cycle, B-cell differentiation, and mouse embryonic stem cell differentiation. We view SPD as a hypothesis generation tool when applied to datasets where the progression is unclear. For example, when applied to a microarray dataset of cancer samples, SPD assumes that the cancer samples collected from individual patients represent different stages during an intrinsic progression underlying cancer development. The inferred relationship among the samples may therefore indicate a trajectory or hierarchy of cancer progression, which serves as a hypothesis to be tested. SPD is not limited to microarray data analysis, and can be applied to a variety of high-dimensional datasets. We implemented SPD using MATLAB graphical user interface, which is available at http://icbp.stanford.edu/software/SPD/.